The subgroup of 4D translations can also be represented by charges in the 2D theory, which act on celestial primary operators via the transformation [1]}
\(\begin{split}\left[P_{m,n},\mathcal {O}_{h, {\bar{h}}}(z, {\bar{z}}) \right]=\frac{1}{2} z^{m+\frac{1}{2}}{\bar{z}}^{n+\frac{1}{2}}\mathcal {O}_{h+ \frac{1}{2}, {\bar{h}}+ \frac{1}{2}}(z, {\bar{z}}),\quad \quad \quad m, n = \pm \frac{1}{2}.\end{split}\) 
